Concordance classes of actions on spheres

1978 ◽  
pp. 85-102
Author(s):  
Michael Davis
Keyword(s):  
Concordance Classes

scholarly journals Smooth and Topological Almost Concordance

2018 ◽  
Vol 2019 (23) ◽  
pp. 7324-7355 ◽  
Author(s):  
Matthias Nagel ◽  
Patrick Orson ◽  
JungHwan Park ◽  
Mark Powell
Keyword(s):  
Homotopy Class ◽  
Infinite Family ◽  
Lens Space ◽  
Free Homotopy Class ◽  
Concordance Classes

Abstract We investigate the disparity between smooth and topological almost concordance of knots in general 3-manifolds Y. Almost concordance is defined by considering knots in Y modulo concordance in Y × [0, 1] and the action of the concordance group of knots in S3 that ties in local knots. We prove that the trivial free homotopy class in every 3-manifold other than the 3-sphere contains an infinite family of knots, all topologically concordant, but not smoothly almost concordant to one another. Then, in every lens space and for every free homotopy class, we find a pair of topologically concordant but not smoothly almost concordant knots. Finally, as a topological counterpoint to these results, we show that in every lens space every free homotopy class contains infinitely many topological almost concordance classes.

scholarly journals Periodicity phenomena for concordance classes of branched coverings

Topology ◽  
1980 ◽  
Vol 19 (3) ◽  
pp. 255-263 ◽  
Author(s):  
Neal Brand ◽  
Gregory Brumfiel
Keyword(s):  
Branched Coverings ◽  
Concordance Classes

scholarly journals Concordance classes of sphere bundles over spheres.

1970 ◽  
Vol 17 (1) ◽  
pp. 57-63
Author(s):  
James R. Munkres
Keyword(s):  
Concordance Classes

scholarly journals Filtering smooth concordance classes of topologically slice knots

2013 ◽  
Vol 17 (4) ◽  
pp. 2103-2162 ◽  
Author(s):  
Tim D Cochran ◽  
Shelly Harvey ◽  
Peter Horn
Keyword(s):  
Concordance Classes

scholarly journals Concordance classes of regular O(n)-actions on homotopy spheres

1980 ◽  
Vol 144 (0) ◽  
pp. 153-221 ◽  
Author(s):  
M. Davis ◽  
W. C. Hsiang ◽  
J. W. Morgan
Keyword(s):  
Concordance Classes

Concordance Classes of Regular U n and Sp n Action on Homotopy Spheres

1977 ◽  
Vol 105 (2) ◽  
pp. 325 ◽  
Author(s):  
M. Davis ◽  
W. C. Hsiang
Keyword(s):  
Concordance Classes

scholarly journals Inertia groups and smooth structures on quaternionic projective spaces

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Samik Basu ◽  
Ramesh Kasilingam
Keyword(s):  
Homotopy Theory ◽  
Projective Spaces ◽  
Stable Homotopy ◽  
High Dimensions ◽  
Stable Homotopy Theory ◽  
Inertia Group ◽  
Smooth Structures ◽  
Concordance Classes

Abstract This paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that the concordance inertia group is trivial in dimension 20, but there are many examples in high dimensions where the concordance inertia group is non-trivial. We extend these to computations of concordance classes of smooth structures. These have applications to 3-sphere actions on homotopy spheres and tangential homotopy structures.

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